Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
598 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21434128 | C2 | semidirect |
| 3. #21427380 | C2 | semidirect |
| 4. #21424927 | C2 | semidirect |
| 5. #21422524 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1486 | C2 | semidirect |
| 216. #1486 | D59 | semidirect |
| 249. C59 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434128 | 2 |
| #21434096 | 2 |
| #21427380 | 2 |
| #21424927 | 2 |
| #21422524 | 2 |
| #21421924 | 2 |
| C59×#1486 | 2 |
| #10013 | 59 |